A probabilistic fatigue lifetime model is developed in conjunction with a multi-scale method for structures with pores whose exact distribution, i.e. geometries and locations, is unknown. The model takes into account uncertainty in fatigue lifetimes in structures due to defects at two scales: micro-scale heterogeneity & meso-scale pores. An element-wise probabilistic strain-life model with its criterion modified for taking into account multiaxial loading is developed for taking into account the effect of micro-scale defects on the fatigue lifetime. The effect of meso-scale pores in the structure is taken into account via statistical modelling of the expected pore populations via a finite element method, based on tomographic scans of a small region of porous material used to make the structure. A previously implemented Neuber-type plastic correction algorithm is used for fast full-field approximation of the strain-life criterion around the statistically generated pore fields. The probability of failure of a porous structure is obtained via a weakest link assumption at the level of its constituent finite elements. The fatigue model can be identified via a maximum likelihood estimate on experimental fatigue data of structures containing different types of pore populations. The proposed method is tested on an existing data-set of an aluminium alloy with two levels of porosity. The model requires lesser data for identification than traditional models that consider porous media as a homogeneous material, as the same base material is considered for the two grades of porous material. Numerical studies on synthetically generated data show that the model is capable of taking into account the statistical size effect in fatigue, and demonstrate that fatigue properties of subsurface porous material are lower than that of core porous material, which makes homogenisation of the model non-trivial.

翻译：本文提出了一种结合多尺度方法的概率疲劳寿命模型，用于处理孔隙精确分布（即几何形状与位置）未知的结构。该模型考虑了结构疲劳寿命在两种尺度缺陷下的不确定性：微观尺度异质性与介观尺度孔隙。为考虑微观缺陷对疲劳寿命的影响，我们建立了单元级概率应变-寿命模型，其准则经修正以考虑多轴载荷作用。结构中介观尺度孔隙的影响则通过统计建模进行考虑：基于用于制造结构的含孔隙材料小区域断层扫描数据，采用有限元方法对预期孔隙群进行表征。采用先前实现的Neuber型塑性修正算法，对统计生成的孔隙场周围应变-寿命准则进行快速全场近似。多孔结构的失效概率通过其组成有限元层面的最弱链假设获得。该疲劳模型可通过包含不同类型孔隙群结构的实验疲劳数据进行最大似然估计辨识。所提方法在具有两种孔隙率水平的铝合金现有数据集上得到验证。由于两种孔隙率等级材料采用相同基体材料，相较于将多孔介质视为均匀材料的传统模型，本模型辨识所需数据量更少。基于合成数据的数值研究表明，该模型能够考虑疲劳中的统计尺寸效应，并证明亚表层多孔材料的疲劳性能低于核心多孔材料，这使得模型的均匀化处理具有非平凡性。